(3x-1)^2/x-1=18x-1/2

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Solution for (3x-1)^2/x-1=18x-1/2 equation:


D( x )

x = 0

x = 0

x = 0

x in (-oo:0) U (0:+oo)

((3*x-1)^2)/x-1 = 18*x-(1/2) // - 18*x-(1/2)

((3*x-1)^2)/x-(18*x)+1/2-1 = 0

((3*x-1)^2)/x-18*x+1/2-1 = 0

(2*(3*x-1)^2)/(2*x)+(-18*2*x*x)/(2*x)+(1*x)/(2*x)+(-1*2*x)/(2*x) = 0

2*(3*x-1)^2-18*2*x*x+1*x-1*2*x = 0

x-18*x^2-12*x-2*x+2 = 0

2-18*x^2-11*x-2*x = 0

2-18*x^2-13*x = 0

2-18*x^2-13*x = 0

2-18*x^2-13*x = 0

DELTA = (-13)^2-(-18*2*4)

DELTA = 313

DELTA > 0

x = (313^(1/2)+13)/(-18*2) or x = (13-313^(1/2))/(-18*2)

x = (313^(1/2)+13)/(-36) or x = (13-313^(1/2))/(-36)

(x-((313^(1/2)+13)/(-36)))*(x-((13-313^(1/2))/(-36))) = 0

((x-((313^(1/2)+13)/(-36)))*(x-((13-313^(1/2))/(-36))))/(2*x) = 0

((x-((313^(1/2)+13)/(-36)))*(x-((13-313^(1/2))/(-36))))/(2*x) = 0 // * 2*x

(x-((313^(1/2)+13)/(-36)))*(x-((13-313^(1/2))/(-36))) = 0

( x-((13-313^(1/2))/(-36)) )

x-((13-313^(1/2))/(-36)) = 0 // + (13-313^(1/2))/(-36)

x = (13-313^(1/2))/(-36)

( x-((313^(1/2)+13)/(-36)) )

x-((313^(1/2)+13)/(-36)) = 0 // + (313^(1/2)+13)/(-36)

x = (313^(1/2)+13)/(-36)

x in { (13-313^(1/2))/(-36), (313^(1/2)+13)/(-36) }

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